[gradsusr] Advection term in the moisture convergence equation

Sat Jan 28 01:52:57 EST 2017

Dear Sir Jeff,

Many many thanks for the help. I got it clearly.

Sincerely,

*Lyndon Mark P. Olaguera*

On Sat, Jan 28, 2017 at 3:38 PM, Jeff Duda <jeffduda319 at gmail.com> wrote:

> Your plot looks correct to me the way you defined it. Whether or not you
> include the '-1' is up to you so long as you understand which sign refers
> to "divergence" and which to "convergence". Traditionally, divergence is
> calculated without the negative sign - in that case convergence has a
> negative value (i.e., convergence is negative divergence). I think the
> choice of whether to use the -1 is a matter of personal preference and/or
> ease of plotting negative contours.
>
> Jeff
>
> On Sat, Jan 28, 2017 at 12:30 AM, Lyndon Mark Olaguera <
> olagueralyndonmark429 at gmail.com> wrote:
>
>> Dear Sir Jeff,
>>
>> Thank you for this wonderful explanation. You are a genius!
>>
>> I have one last question regarding the sign of the output attached in
>> this email.
>>
>> Here's the script that I am using.
>>
>> 'sdfopen pentad_ensmean_shum_1981-2010.nc'
>> 'sdfopen ../uwind/pentad/pentad_ensmean_uwind_1981-2010.nc'
>> 'sdfopen ../vwind/pentad/pentad_ensmean_vwind_1981-2010.nc'
>> 'set dfile 1'
>> 'define q=shum(z=3)'
>> 'set dfile 2'
>> 'define u=uwnd(z=3)'
>> 'set dfile 3'
>> 'define v=vwnd(z=3)'
>> 'color -0.2 0.2 0.02 -kind blue->white->red'
>>
>> *'define mconv=(-1)*hdivg(u*q,v*q)*1e6'*
>>
>>
>> 'set lat -5 45'
>> 'set lon 80 180'
>> 'd mconv'
>> 'xcbar -fs 2'
>>
>> *overlay 850mb winds
>> 'set gxout vector'
>> 'set arrscl 0.3 10'
>> 'd u;v'
>>
>>
>> Question:
>>
>> 1. I overlayed the 850 mb winds over the calculated MFC, but the results
>> do not match. I'm not sure if I understand this correctly.
>> From the defined mconv equation, negative values should correspond to
>> "convergence", while positive values should correspond to "divergence".
>> But in the attached image, positive values are seen over areas of
>> convergence. Is the correct equation for the MFC above should contain -1 or
>> this depends on the situation?
>>
>>
>> *Lyndon Mark P. Olaguera*
>>
>>
>> On Sat, Jan 28, 2017 at 2:53 PM, Jeff Duda <jeffduda319 at gmail.com> wrote:
>>
>>> Lyndon,
>>> Absolutely. I calclulate MFC frequently. Use cdiff. But before I give
>>> the full explanation, I should note that your formula already gives the
>>> full MFC field. hdivg(q*u,q*v) should include the advection term. You can
>>> verify this by comparing that formula to those below that I will give you.
>>>
>>> The trick with this is to define your grid spacing before doing anything
>>> else. While your model integration may use a fixed grid spacing (whether in
>>> degrees or linear distance or otherwise), if you use a control file to
>>> display the data, and if it includes XDEF and YDEF entries, then the grid
>>> on which your data are calculated may differ from that on which the model
>>> was integrated, so you can't use your scalar grid spacing value in that
>>> case. You can define your data grid spacing using trigonometry. The
>>> equations to calculate that are
>>>
>>> dx = Re * cos(lat) * cdiff(lon,x)
>>> dy = Re * cdiff(lat,y)
>>>
>>> In the above equations, Re is the radius of the earth, and you need to
>>> make sure to convert between radians and degrees. Grads functions assume
>>> inputs are in radians and also output in radians. However, the lat and lon
>>> fields are in degrees, so convert. Both formulas are also instances of the
>>> arc length formula for a circle, which assumes the angle is in radians. So
>>> basically, convert everything to radians in those equations.
>>>
>>> Once you have those terms, you have all the fields you need (assuming
>>> you have mixing ratio and wind components defined on the same grid already):
>>>
>>> advection term = -u * cdiff(q,x) / dx - v * cdiff(q,y) / dy
>>> convergence term = q*hdivg(u,v)
>>>
>>> To verify that the advection term is already contained in
>>> hdivg(q*u,q*v), it should suffice to display
>>> hdivg(q*u,q*v) - q * hdivg(u,v)
>>> This field should match the advection term field above. You can also
>>> display
>>> hdivg(q*u,q*v) - q * hdivg(u,v) - [ -u * cdiff(q,x) / dx - v *
>>> cdiff(q,y) / dy] and it should be 0.
>>>
>>> I might be wrong about this since the divergence operator in spherical
>>> coordinates includes an additional term to represent convergence for purely
>>> meridional wind, so you may want to crack open a dynamics textbook and find
>>> what that term is and include it in here somewhere. Either way, I hope this
>>> helps.
>>>
>>> Jeff Duda
>>>
>>> On Fri, Jan 27, 2017 at 11:35 PM, Lyndon Mark Olaguera <
>>> olagueralyndonmark429 at gmail.com> wrote:
>>>
>>>> Dear All,
>>>>
>>>> I'm trying to calculate the moisture flux convergence using the
>>>> following commands:
>>>>
>>>> *At 850 mb
>>>>
>>>> 'set dfile 1'
>>>> 'define q=shum(z=3)'
>>>>
>>>> 'set dfile 2'
>>>> 'define u=uwnd(z=3)'
>>>>
>>>> 'set dfile 3'
>>>> 'define v=vwnd(z=3)'
>>>>
>>>> 'color -0.2 0.2 0.02 -kind blue->white->red'
>>>> 'define mconv=(1)*hdivg(u*q,v*q)*1e6'
>>>>
>>>> According to this link, I have to add the advection term.
>>>>
>>>> http://www.spc.noaa.gov/publications/banacos/mfc-sls.pdf
>>>>
>>>> [image: Inline image 1]
>>>>
>>>> Question:
>>>>
>>>> 1. Is there a way to do this in grads?
>>>> 2. Or is there a function in GRADS that can calculate partial
>>>> derivatives?
>>>>
>>>> I'll appreciate any help.
>>>>
>>>> Best,
>>>>
>>>> *Lyndon Mark P. Olaguera*
>>>>
>>>>
>>>> _______________________________________________
>>>> gradsusr mailing list
>>>> gradsusr at gradsusr.org
>>>> http://gradsusr.org/mailman/listinfo/gradsusr
>>>>
>>>>
>>>
>>>
>>> --
>>> Jeff Duda
>>> Post-doctoral research fellow
>>> University of Oklahoma School of Meteorology
>>>
>>> _______________________________________________
>>> gradsusr mailing list
>>> gradsusr at gradsusr.org
>>> http://gradsusr.org/mailman/listinfo/gradsusr
>>>
>>>
>>
>> _______________________________________________
>> gradsusr mailing list
>> gradsusr at gradsusr.org
>> http://gradsusr.org/mailman/listinfo/gradsusr
>>
>>
>
>
> --
> Jeff Duda
> Post-doctoral research fellow
> University of Oklahoma School of Meteorology
>
> _______________________________________________
> gradsusr mailing list
> gradsusr at gradsusr.org
> http://gradsusr.org/mailman/listinfo/gradsusr
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://gradsusr.org/pipermail/gradsusr/attachments/20170128/c60dbcb8/attachment-0001.html 
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 11693 bytes
Desc: not available
Url : http://gradsusr.org/pipermail/gradsusr/attachments/20170128/c60dbcb8/attachment-0001.png 